(2x-5)(2x-5)=9

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Solution for (2x-5)(2x-5)=9 equation: 


Simplifying
(2x + -5)(2x + -5) = 9

Reorder the terms:
(-5 + 2x)(2x + -5) = 9

Reorder the terms:
(-5 + 2x)(-5 + 2x) = 9

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) = 9
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 9
((25 + -10x) + 2x * (-5 + 2x)) = 9
(25 + -10x + (-5 * 2x + 2x * 2x)) = 9
(25 + -10x + (-10x + 4x2)) = 9

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) = 9

Solving
25 + -20x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
25 + -9 + -20x + 4x2 = 9 + -9

Combine like terms: 25 + -9 = 16
16 + -20x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
16 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -5x + x2) = 0

Factor a trinomial.
4((1 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}

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